Because Microsoft asks that PDF's be Accessible, it means that the PDF needs to be run through Acrobat.
When running through the Accessibility Action Wizard in Acrobat, it adds the "A" to the end of most sentences (not all) but also many words sprinkled over the page, as you can see above.
I'm wondering if it is some sort of Glyph glitch? I know when I use Mona in Illustrator, for example, select a word, head to Character and change from Helvetica to Mona, the Glyph panel will immediately show up. Wondering if the "A" is replacing the broken glyph, even if it's only a space.
See here for Export out of InDesign, and after running Accessibility.
Reporting via @Jobey-G, who's having this issue.
Exported and seen through Acrobat: